The New Sudoku Players' Forum

by **doduff** » Fri Jun 02, 2006 9:48 pm

Here is a puzle from the top50000 which I got of some other site.

Code: Select all: *-----------* |.6.|...|..9| |...|7.1|2..| |..3|.2.|...| |---+---+---| |.54|3..|...| |8..|.1.|..2| |...|..9|86.| |---+---+---| |...|.4.|3..| |..6|5.8|...| |7..|...|.1.| *-----------* *-----------* |.6.|8..|..9| |...|761|2..| |..3|92.|...| |---+---+---| |654|382|...| |8..|61.|..2| |...|4.9|86.| |---+---+---| |...|14.|3..| |..6|5.8|.2.| |7..|2..|.1.| *-----------* *-----------------------------------------------------------------------------* | 1245 6 1257 | 8 35 345 | 1457 457 9 | | 459 489 589 | 7 6 1 | 2 3458 3458 | | 145 1478 3 | 9 2 45 | 14567 4578 145678 | |-------------------------+-------------------------+-------------------------| | 6 5 4 | 3 8 2 | 179 79 17 | | 8 379 79 | 6 1 57 | 45 345 2 | | 123 1237 127 | 4 57 9 | 8 6 35 | |-------------------------+-------------------------+-------------------------| | 259 289 2589 | 1 4 67 | 3 5789 5678 | | 134 134 6 | 5 379 8 | 479 2 47 | | 7 34 589 | 2 39 36 | 4569 1 4568 | *-----------------------------------------------------------------------------*

There is a seemingly continuous multiple inference loop here:

[r8c5]=7=[r6c5](-7-[r5c6]-5-[r3c6]-4-[r1c6])=5=[r1c5]-5-[r1c6]-3-[r9c6]-6-[r6c6]-7-[r8c5] => [r1c1367]<>5 ?

The weak(-5) inference in row 1 wants to be a strong(3) inference it seems like, but this would destroy continuity, if this is continuous that is.

Any thoughts?

It seems like no eliminations can be made from this loop. Using the rule for double implication chains, I want to eliminate the 5's from row 1, and although this is a valid elimination, does the loop above allow me to do so?

by RW » Fri Jun 02, 2006 10:30 pm

When uncertain, the question you should ask yourself is: If r1c1, r1c3, r1c6 or r1c7=5, would it cause a contradiction when I try to fill the mentioned cells? If the answer is yes, then the elimination is valid. If the answer is no, then you cannot eliminate the candidates unless you expand your loop to other cells. I had no problem assigning the value 5 to all of the four cells (one at a time of course) and then fill in the cells you mentioned in your loop without causing any contradictions => eliminations are not valid.

RW

by **doduff** » Sat Jun 03, 2006 12:14 am

AH.. thats a good check. Thanks.

by **daj95376** » Sat Jun 03, 2006 4:07 am

Code: Select all: *-----------------------------------------------------------------------------* | 1245 6 1257 | 8 35 345 | 1457 457 9 | | 459 489 589 | 7 6 1 | 2 3458 3458 | | 145 1478 3 | 9 2 45 | 14567 4578 145678 | |-------------------------+-------------------------+-------------------------| | 6 5 4 | 3 8 2 | 179 79 17 | | 8 379 79 | 6 1 57 | 45 345 2 | | 123 1237 127 | 4 57 9 | 8 6 35 | |-------------------------+-------------------------+-------------------------| | 259 289 2589 | 1 4 67 | 3 5789 5678 | | 134 134 6 | 5 379 8 | 479 2 47 | | 7 34 589 | 2 39 36 | 4569 1 4568 | *-----------------------------------------------------------------------------*

Setting [r6c5]=5 leads to a cascade of singles that solve the puzzle. Unfortunately, setting [r6c5]=7 and getting a contradiction is outside my reach. Ack!

by **doduff** » Sat Jun 03, 2006 6:19 am

I have tried so many different chains. They are all so long and complicated. I feel like there should be come reasonable chain that I can get something out of. I just can't find it!!!!

I played with r6c5 for a long time and came up with only continuous loops that lead to no eliminations or single chains that lead nowhere and can't be connected in any obvious way(to me at least).

Maybe some one will grace me with a next step!

by **Carcul** » Sun Jun 04, 2006 10:57 am

Code: Select all: *------------------------------------------------------* | 1245 6 1257 | 8 35 345 | 1457 3457 9 | | 459 489 589 | 7 356 1 | 2 3458 34568 | | 145 1478 3 | 9 2 456 | 14567 4578 145678 | |------------------+-------------+---------------------| | 6 5 4 | 3 8 2 | 179 79 17 | | 8 379 79 | 6 1 57 | 45 345 2 | | 123 1237 127 | 4 57 9 | 8 6 35 | |------------------+-------------+---------------------| | 259 289 2589 | 1 4 67 | 3 5789 5678 | | 134 134 6 | 5 379 8 | 479 2 47 | | 7 34 589 | 2 369 36 | 4569 1 4568 | *------------------------------------------------------*

1. [r2c5]=6=[r2c9]=3=[r6c9]=5=[r6c5](-5-[r2c5])-5-[r1c5]
-3-[r2c5], => r2c5<>3,5.

2. [r89c7]-4-[r5c7]=4=[r5c8]=3=[r6c9]=5=[r6c5]=7=[r8c5]
-7-[r8c9]-4-[r89c7], => r8c7/r9c7<>4.

3. [r6c2]=2=[r7c2]-2-[r7c3]=2|7=[r5c3]-7-[r6c2], => r6c2<>7.

4. [r3c7]=6=[r9c7]-6-[r7c9]=6=[r7c6]=7=[r5c6]-7-[r5c2]=7=
[r3c2]-7-[r3c7], => r3c7<>7.

5. [r2c9]=3=[r6c9]=5=[r6c5]=7=[r5c6]-7-[r5c2]=7=[r3c2]=8=
[r2c23]-8-[r2c9], => r2c9<>8.

6. [r1c1]=2=[r1c3]=1=[r6c3]=7=[r6c5]=5=[r1c5]-5-[r1c13],
=> r1c1/r1c3<>5.

7. [r1c78]-5-[r2c9]=5=[r6c9]-5-[r6c5]=5=[r1c5]-5-[r1c78],
=> r1c7/r1c8<>5.

8. [r7c9]=6=[r7c6]=7=[r5c6](=5=[r5c78]-5-[r6c9]=5=[r2c9]
-5-[r2c3])-7-[r5c3]-9-[r2c3]-8-[r9c3]=8=[r9c9]-8-[r7c9],
=> r7c9<>8.

9. =4=[r2c2]-{Nice Loop: [r9c3]-8-[r7c2]=8=[r3c2]-8-[r3c9]
=8=[r9c9]-8-[r9c3]}-8-[r9c3]=8=[r9c9]=4=[r9c2]-4-[r2c2],
=> r2c2<>4.

10. [r7c2]-9-[r7c1]=9=[r2c1]=4=[r1c1]=2=[r1c3]-2-[r7c3]=2|7=[r5c3]
=9=[r5c2]-9-[r7c2], => r7c2<>9.

11. [r7c3]=2|7=[r5c3]=9=[r5c2]-9-[r2c2]-8-[r7c2]-2-[r7c3],
=> r3c2<>8; r7c1<>2.

12. [r3c8]=8=[r7c8]-8-[r7c2]-2-[r7c3]=2|7=[r5c3]-7-[r5c2]=7=
[r3c2]-7-[r3c8], => r3c8<>7.

13. [r4c8]=9=[r7c8]-9-[r7c1]=9=[r2c1]=4=[r1c1]-4-[r1c8]-7-
[r4c8], => r4c8<>7.

14. [r6c1]=2=[r1c1]=4=[r2c1]-4-[r2c8]=4=[r5c8]=3=[r5c2]
-3-[r6c1], => r6c1<>3.

15. [r6c5]-7-[r6c3]=7|4=[r1c1]-4-[r1c7]-1-[r4c7]-7-[r8c7]=7=
[r8c5]-7-[r6c5], => r6c5<>7 and the puzzle is solved.

In step "9" I have used an Almost Nice Loop.

Carcul

by **Jeff** » Sun Jun 04, 2006 1:06 pm

Previous post deleted due to incorrect strong link drawn.
Thanks Carcul.

Here is another one:

by **Carcul** » Sun Jun 04, 2006 1:13 pm

Hi Jeff.

Nice to see you around here. Just to note that, in your b/b plot, the strong link "[r1c3]=1=[r5c3]" is wrong: it should be "[r1c3]=1=[r6c3]".

Regards, Carcul

by **doduff** » Fri Jun 09, 2006 3:42 am

Thanks for the help.

I found some cool chains. Here is one I am particularly proud of, but don't know how would be the best way to notate it.

Code: Select all: State if the puzzle: *--------------------------------------------------------------------* | 1245 6 127 | 8 35 345 | 1457 457 9 | | 459 489 589 | 7 6 1 | 2 3458 358 | | 145 178 3 | 9 2 45 | 14567 4578 15678 | |----------------------+----------------------+----------------------| | 6 5 4 | 3 8 2 | 17 9 17 | | 8 379 79 | 6 1 57 | 45 345 2 | | 123 1237 127 | 4 57 9 | 8 6 35 | |----------------------+----------------------+----------------------| | 259 289 2589 | 1 4 67 | 3 578 5678 | | 134 134 6 | 5 379 8 | 79 2 47 | | 7 34 58 | 2 39 36 | 569 1 4568 | *--------------------------------------------------------------------*

============

Chains:

If [r2c9]=3 => [r6c9]=5 => [r379c9]<>5

If [r2c9]=5 => [r379c9]<>5

If [r2c9]=8 => [r2c123]<>8 and is locked on 459 => [r136c1]<>45 and is locked on 123 => [r6c9]<>3 and is thus 5 so [r379c9]<>5

So [r379c9]<>5

============

Maybe write like this:

[r379c9]-5-[r6c9]-3-[r2c9]-{ANL:[r2c9]-5-[(r6c9)]-3-[ALS:r5c78]=3=[r5c2]-3-[almostALS:r136c1]=3|8=[ALS:r2c123]-8-[r2c9]}-5-[r379c9] => [r79c9]<>5

Where there is an almost almost locked set in there. Does that notation make sense?

I have since found a few more loops but still need about 9 more eliminations to match Carcul's solution.

Now let me ask this: Carcul, how do you go about finding your chains? Do you have any special techniques that you would like to share?

Thanks,Joe

by **Carcul** » Fri Jun 09, 2006 8:35 am

Hi Doduff.

I am pleased to see that finally someone decided to try to use the ANL concept. However, you use it in a somewhat confusing fashion and it is more simple to write the deduction without the ANL. Check this:

[r379c9]-5-[r6c9](-3-[r2c9])-3-[r1236c1|r2c23]=3|8=[r2c23]-8-[r2c9]-5-
-[r379c9], => r3c9/r7c9/r9c9<>5.

Carcul

by **daj95376** » Fri Jun 09, 2006 9:16 am

If you allow chains to resolve Naked/Hidden Singles, then the original puzzle can be solved as follows.

Code: Select all: r4c5 = 8 Hidden Single r4c1 = 6 Hidden Single r4c6 = 2 Hidden Single r6c4 = 4 Naked Single r1c4 = 8 Naked Single r5c4 = 6 Naked Single r3c4 = 9 Naked Single r9c4 = 2 Naked Single r7c4 = 1 Naked Single b6 - 179 Naked Triple b7 - 134 Hidden Triple r8c8 = 2 Hidden Single r9c2 = 4 [r9c2]=3 => [r5c3]=EMPTY r8 - 13 Naked Pair r9c6 = 3 [r9c6]=6 => [r9]=INVALID r9c5 = 9 [r9c5]=6 => [c7]=INVALID trivial from here

If you only allow chains to resolve Naked Singles, then the original puzzle can be solved as follows.

Code: Select all: r4c5 = 8 Hidden Single r4c1 = 6 Hidden Single r4c6 = 2 Hidden Single r6c4 = 4 Naked Single r1c4 = 8 Naked Single r5c4 = 6 Naked Single r3c4 = 9 Naked Single r9c4 = 2 Naked Single r7c4 = 1 Naked Single b6 - 179 Naked Triple b7 - 134 Hidden Triple r8c8 = 2 Hidden Single r9c5 <> 3 [r9c5]=3 => [r9]=INVALID r9c5 = 9 [r9c5]=6 => [c7]=INVALID r8c7 = 9 Hidden Single r4c8 = 9 Hidden Single r2c5 = 6 Hidden Single b2 - 3 Locked Candidate (1) r5c3 = 9 [r5c3]=7 => [r8c1]=EMPTY c3 - 58 Naked Pair r7c3 = 2 Naked Single r1c1 = 2 Hidden Single r6c2 = 2 Hidden Single r9c6 = 3 [r9c6]=6 => [c3]=INVALID trivial from here

by **doduff** » Fri Jun 09, 2006 4:42 pm

Ah... That is a much batter way to denote it. I think the shorter the notation, then the better the chain.

Carcul wrote:[r379c9]-5-[r6c9](-3-[r2c9])-3-[r1236c1|r2c23]=3|8=[r2c23]-8-[r2c9]-5-
-[r379c9], => r3c9/r7c9/r9c9<>5.

Although I did group my cells just slightly 'differently'. -[r136c1|r2c123]=3|8=[r2c123]- instead of -[r1236c1|r2c23]=3|8=[r2c23]- but they are equivalent in some sense. I guess if one can avoid using an almost nice loop, then that should be the case. An almost nice loop should be used if it makes the chain clearer. I did feel that there was something funny about the way I did it.

Here is another use of an almost nice loop, but this one is way long and I kind of lucked out that it worked. I was going for an eliminations somewhere else, but found an error in my reasoning, but luckily it was fixed by changing only 3 links.

Code: Select all: The state of the puzzle: *-----------------------------------------------------------* | 1245 6 127 | 8 35 345 | 147 47 9 | | 459 489 589 | 7 6 1 | 2 3458 35 | | 145 178 3 | 9 2 45 | 156 4578 1678 | |-------------------+-------------------+-------------------| | 6 5 4 | 3 8 2 | 17 9 17 | | 8 379 79 | 6 1 57 | 45 345 2 | | 123 1237 127 | 4 57 9 | 8 6 35 | |-------------------+-------------------+-------------------| | 259 289 2589 | 1 4 67 | 3 578 678 | | 134 134 6 | 5 379 8 | 79 2 47 | | 7 34 58 | 2 39 36 | 569 1 468 | *-----------------------------------------------------------*

The 'Loop':
[r3c9](-7-[r8c9]-4-[ALS:r8c12]=4=[r9c2])-7-[r4c9]=7=[r4c7]-7-[r8c7]-9-[r9c7]=9=[r9c5]=3=[r9c6]=6=[r7c6]=7=[r5c6]=5=[r6c5]-{ANL:[r6c3]=7=[r6c2]-7-[r3c2]=7=[r1c3]=1=[r6c3]}-2-[r16c3]=2=[r7c3]-2-[r7c2]=2=[r6c2]=7=[r6c3]=1=[r1c3]-1-[ALS:r1c7|r1c8]-7-[r3c9] => [r3c9]<>7

Basically what I did was test each 3 in [r9c356]. Feel free to go through this loop and write it better too!

Thanks for the help!

daj: What do you mean by "only allowing chains to resolve naked/hidden singles"?

The New Sudoku Players' Forum

Continuous multiple inference loop?

Continuous multiple inference loop?

Here is a possible solution